Unit Status

Units exist in 3 main states:

Good Order

As soon as a unit 'takes a hit', its counts as being Disordered, and it's effectiveness is reduced. This means it deducts 1 from any die rolls where it is trying to inflict damage on the enemy.
Because this only counts when the unit is trying do inflict damage, the effects of Disorder do not count when making 'defensive' die rolls where it is the target of enemy shooting (Unlike in DBM, shooting is always diced for as shooter vs target, there is no mutual shooting in a single roll in ADLG).
Each unit can take a number of hits before it is removed from play. Close formation infantry start on 4 hits, so the 4th hit kills them, Medium Infantry, Cavalry, Knights and Elephants start with 3, and Skirmishers have only 2 hits before they are gone.
The most common type of marker is the traffic light system - red for 3 hits, amber for 2, green for 1. Some folks work backwards, and have red for 'one hit until they are dead', but that can be confusing.
Disorder from hits is different to the effects caused by terrain. Terrain causes a combat disadvantage, but it does not do permanent damage and is not "Disorder".
You can also take Disorder by withdrawing from combat or reversing out of a ZOC in certain situations.
You can Rally off hits using your Generals command points/pips. It's harder when the unit is in combat, and easier (as in, costs no pips to try) when you are more than 4MU away from any enemy. A good reason to withdraw your skirmishers after they have done their job!

Otherwise known as dead, or removed from play.
Routed non-skirmish units cause a hit on any friends 1MU or less immediately behind them, so don't get your reserves too close!
Routed Elephants can cause damage in all directions, in an Elephant Rampage!